Being chased in a dream usually points to something you're avoiding rather than an outside threat -- an unresolved conflict, an emotion, or a truth that keeps catching up no matter how fast you move. Turning to face whatever's chasing you, even in the dream, often marks a readiness to deal with it directly.
The first sign hath pre-eminence in signification, when there be two signs have to do with the thing. - William Lilly (1602.-1681.)